The Fox TV network is considering replacing one of its prime-time crime investig

Question

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 450 viewers. After viewing the comedy, 200 indicated they would watch the new show and suggested it replace the crime investigation show.

Develop a 99% confidence interval for the population proportion. (Use z Distribution Table.) (Round the z-values to 2 decimal places. Round your answers to 3 decimal places.)

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 450 viewers. After viewing the comedy, 200 indicated they would watch the new show and suggested it replace the crime investigation show.

Explanation / Answer

Given :-. N = 450 , x= 200

P= (x/N) = 200/450 = 0.445 is a value for population proportion

When does not gives Po then we gaves us 0.5

SE= (Po*(1-Po)/N) = 0.5*0.5/450 = 0.0234

Z = ( P - Po )/ SE

= (0.445 - 0.5) / 0.0234

Z = - 2.35

99% confidence interval for the population proportion

( P - Z /2 *( P*(1-P)/N) , P + Z /2 *( P*(1-P)/N) )

P= 0.445 , Z /2 = 99% then critical value is 2.576

( P*(1-P)/N) = (0.445 *0.555 /450) = 0.02340

( 0.445 - 2.576*0.02340 , 0.445 +2.576*0.02340)

(0.445 - 0.0602784 , 0.445 + 0.0602784)

( 0.384 , 0.505) round up answer.

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